For a polynomial p(x) = anx" + an-1xn-1 +... + a₁x + ao with a; E F and square matrix A with entries in F, define p(A) by p(A) = an A+an-1A-1 + + a₁A+aoI. Let A € Mnxn(C) be diagonalizable and c(x) the characteristic polynomial of A. Then show (ie, prove) that c(A) = 0, where O is the n x n zero matrix.

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